Jan Lester believes that I have not been able to cross the epistemological pons asinorum of leading to comprehension of Sir Karl Popper's doctrine of falsificationism. To the contrary, I contend that I both have crossed that bridge and moved on down the road beyond it.

At the heart of our dispute is Popper's bold attempt to create a theory of science that, while acceding to the sceptical arguments against induction, still holds that science is both a rational and pragmatically useful enterprise. Popper tried to traverse a razor's edge path along a high ridge running between the two broad plains presenting less arduous approaches to conceiving science. On one side, denying any validity to induction clears the way to a full-blown skepticism about the claim that science yields any genuine knowledge about the world we occupy. On the other, a pilgrim could join with most scientists and many philosophers in regarding reliance on induction as an essential aspect of how science moves closer and closer to the truth.

The issue at hand is whether or not Popper was able to maintain his balance and chart a reliable course above the two threatening precipices. I will argue that he was not, and that, faced with cogent criticisms of his system, he even allowed inductive inference back into polite scientific company, although he could never bring himself to re-introduce the returnee by name.

Karl Popper

Induction Is a Valid Tool of Science

Popper's case against induction is based on the valid insight that observations of individual cases where some proposition is true, no matter how numerous, are ever enough to demonstrate that it is always true. Lester puts the case as follows:

"Given that we do not have an omniscient god's-eye view of the universe, we cannot, in principle, perceive the truth of universal propositions such as ‘All Swans are white' (where that includes all past, present and future swans). Neither could any finite number of observations of white swans (even if they could be guaranteed to be accurate, which they cannot) add any strength to the universal theory that they are all white: for the observations are, ex hypothesi, an infinitely small number relative to the universal theory. So we cannot even make our theories more probable (except on the basis of assumptionsconjectures about probability that cannot be shown to be independently probable). However, says Popper, nil desperandum. There is an asymmetry between verification and falsification. We could, in principle (though we might always be mistaken), perceive a single non-white swan. And if we in fact (as a matter of reality) do so then that fact would, as a logical implication, falsify the theory that all swans are white."

But Hume, and Popper and Lester after him, have mistakenly conflated the idea that repeatedly witnessing some event B follow some event A means that B will always follow A, which we might call naïve inductivism, with inductivism tout court . Naïve inductivism contends that having seen only white swans lends credence to a law stating that all swans are white. However, that type of inductive inference was denigrated as the flawed method embraced by his Aristotelian opponents by one of Popper's prime exemplars of inductivism, Francis Bacon . As Adolf Grünbaum notes, "Bacon made a vital contribution toward distinguishing merely positive from supportive instances of a theory by emphasizing that some kinds of positive instances can differ radically from others in evidential value... (1976, p. 217). The especially supportive instances Bacon had in mind are essentially what Popper called risky predictions. Grünbaum continues, "Bacon... rejected induction by simple enumeration of positive instances as puerile" (1976, p. 219). Bacon declared: "To conclude upon an enumeration of particulars, without instance contradictory, is no conclusion but a conjecture" (quoted in Quinton, 1980, p. 51). Bacon's follower, the great philosopher of experimental methodology Robert Boyle, recognized that "a thousand experiments or observations made to confirm a theory do not have the force of one made to prove the contrary" (Sargent, 1995, p. 145). Two hundred years later, we find "the confirmed inductivist J.S. Mill... denies the probative value of mere repetition of positive instances just as much as Popper does..." (Grünbaum, 1976, p. 219). And the greatest of American philosophers, C.S. Peirce, called induction by enumeration "crude induction," even while originating the idea that inference to the best explanation, which he called abduction and which involves inductive reasoning, is the essence of how scientists choose among competing theories (Misak, 2000, p. 338).

As noted above, Popper failed to comprehend the difference between naïve and sophisticated inductivism, demonstrating his ignorance in quotes like the following: "The fundamental doctrine which underlies all theories of induction is the doctrine of the primacy of repetitions.... (quoted in Grünbaum, 1976, p. 220). As Grünbaum concludes, "Popper was seriously mistaken in claiming that IN THE ABSENCE OF NEGATIVE INSTANCES, all forms of inductivism are necessarily committed to the (probabilified) scientific credibility of a theory, merely because that theory can adduce numerous positive instances" (Grünbaum, 1976, p. 229, upper case in original).

So if, in the sophisticated view, the mere repetition of some sequence of events is not sufficient ground for inductive inference, then what is? Bacon (who was a lawyer by profession), Boyle, and Kant all regarded arguing for a scientific theory as analogous to arguing a legal case. As Ernst Cassirer says of Kant's view of induction, "Accidental observations, made in obedience to no previously thought-out plan, can never be made to yield a necessary law… Reason… must not [approach] nature in the character of a pupil… but of an appointed judge who compels the witness to answer questions which he himself has formulated" (1981, p. 163). Neither side in a courtroom dispute can ever hope to demonstrate the truth of their version of events with the certainty of a purely deductive argument or a proof in mathematics. Everyone involved ought to be aware that any verdict reached on the basis of the evidence available is fallible -- it may later be discovered that the DNA found at the crime scene was not that of the man who was convicted of the crime, so that the verdict must be overturned. But that is no reason to conclude that juries never arrive at the correct verdict. Furthermore, in their attempt to reach a conclusion, jurors quite reasonably consider not only whether either party was able to disprove (falsify) the case of the other, but also whatever positive (confirming) evidence for the defendant's guilt or innocence was presented.

Robert Boyle

Boyle recommended induction as an integrated part of a broader search for a scientific explanation -- an exploration also employing falsification, deductive logic, a quest for simplicity, an inclination towards what seems plausible, and the knowledge gained from previous quests, one "that seeks out the invisible corporeal agents that give rise to the qualities of bodies" (quoted in Sargent, 1995, p. 162). After having hypothesized the existence of some such agent as a plausible cause of the phenomena under investigation, it is quite reasonable for a scientist to increase her confidence in her theory when she finds her experiments yield the results called for by it. She is not reasoning from the bare fact that every swan she has seen was white to the generalization that all swans are so; instead, she believes, for instance, that she has discovered a genetic feature of swans that will always bring about white feathers, and, quite sensibly, she regards encountering thousands of swans, all of which are white, as evidence that she may be on to something. And notice that in the latter case, discovering a black swan need not even be taken to falsify her theory -- perhaps this swan was conceived just after the nuclear explosion at Chernobyl, and she only needs to add the proviso (see Hempel, 1988), "unless the swan has wildly abnormal genes."

As an aid in comprehending Boyle's conception of science as similar to an investigation and trial seeking to convict the "guilty" causal factor of being responsible for some class of observed phenomena, we might imagine that we are the jury in a rape trial. In making its case, the prosecution notes that the defendant previously has been convicted of rape five times, and that each of those rapes had numerous features -- perhaps the rapist's method, the time of day, the appearance of the victim -- similar to the crime under deliberation. Those facts certainly do not constitute logical proof of the defendant's guilt, which is the standard Popper sets for inductive inference. Nevertheless, it seems entirely rational for the jurors to regard such evidence as strengthening the prosecution's case. The previous instances are not being used to argue that, simply because something happened often in the past, it will keep on happening. Instead, they suggest the presence of a causal factor: the defendant is the sort of person who will commit rape, and in a way similar to the crime presently being prosecuted.

If the above seems awfully littered with quotes and references for a web article, that is partly explained because they demonstrate that Lester is either grossly ignorant of the history of philosophy or being disingenuous when he writes:

"It is quite confused of Callahan to think it is Popper's situational logic (as I have called it) that has supposedly demolished inductivism. Induction had long been shown to be a fallacy for the simple reason that it goes beyond the evidence. David Hume (1711-1776) is the, relatively, modern person who rediscovered and emphasised the fallacy."

Since Hume wrote on induction, many – indeed, probably most -- philosophers have argued against his conclusion. Immanuel Kant, J.S. Mill, C.S. Peirce, Hans Reichenbach, and Carl Hempel have been among the prominent thinkers who have decided Hume did not have the final word on the topic. More recently, a number of Popper's own followers, including Paul Feyerabend, Imre Lakatos, and John Worrall have embraced Popper's verdict on induction only to later acknowledge its proper role in science . But, if it's true that I am "quite confused" in thinking that Popper claimed to be making a breakthrough on the topic of induction, then at least I am not alone: "I think I have solved a major philosophical problem: the problem of induction…" -- Sir Karl Popper (1972, p. 1)

Popper Could Not Avoid Induction

So far, I have been arguing that inductive inference, when employed sensibly, with caution and humility, has a valid role in the evaluation of scientific theories. Now I will examine the criteria for choosing among competing theories with which Popper attempted to replace induction. Given his admiration for science and his view that it is an eminently rational activity, he naturally sought to bridge the gaps created by banishing induction. For example, why should we turn to science when making predictions? As pointed out by Wesley C. Salmon (1988), Popper executed elaborate contortions in trying to provide an answer that did not involve induction. He suggested that a theory, by surviving a stringent test aimed at falsifying it, became better corroborated -- not confirmed Such passing marks neither should lead us to think that the theory receiving them is in any sense true -- Popper argued that the probability of any theory being true is nil -- nor, as investment firms are fond of saying, should past performance be regarded as indicative of future results. Nevertheless, given that the best corroborated theory about some class of phenomena so far had withstood all scientific -- i.e. rational -- criticism, it was the only rational means available for making predictions regarding future events falling within the scope of that current champion. However, Salmon asks why it would be rational to base predictions on currently accepted scientific ideas if previous corroboration of a law or model should not increase our belief in its continued success from here on out. The mere rationality of some activity regarded on its own says nothing about whether it is rationally used as a means to some end. Chess is a rational pastime, but that doesn't imply that it is rational to use chess results to forecast the weather. Discussing Aristotle's system of logic may fully engage one's reason, but that does not mean it is a reasonable method to choose for seducing a potential lover or for soothing a howling infant. And Salmon counters the Popperian response that "we have nothing else to go on" but today's best science by noting it is obviously untrue, since we could decide to read tea leaves or examine the inner organs of chickens instead. If all inductive inference from a historical record of success to a high likelihood of similar results when using the theory tomorrow is fallacious, then it is no less rational to consult an astrologer or palm reader than an engineer when designing a new bridge.

So, in trying to argue for the rationality of scientific prediction within his methodology, Popper essentially wound up admitting induction into his system under the new name "corroboration." However, an even more damaging indictment of his approach is that falsification itself depends on inductive inferences, since, if a scientist cannot regard experience as offering even limited and qualified guidance about the probable course of coming events, then he has no basis for holding that some new experiment or observation has disproved a theory. For one thing, no measurement is ever perfect. How, then, can the falsificationist decide whether a theory has been falsified or if it was the contradictory measurement that was in error? The typical solution is to consider previous tests of the reliability of the measuring device to establish its likely margin of error, but a Popperian should reject that answer, since it clearly relies on inductive inference in extrapolating from the past performance of a device to the present case. And it is pointless to repeat the potentially falsifying experiment to see if the result holds, for the idea that the repetition of a result lends it increased credibility is again inductive As Kyberg notes: "The theory of measurement is not only a proper theory, it is a theory that cannot be refuted in any simple way by a contrary observation, and this deductive awkwardness immediately spreads to the testing of any quantitative law" (1988, p. 70).

What's more, there is no possibility of testing all of our ideas at the same time. As a result, any test purporting to falsify one theory will always rely on the past success of other theories as a valid indication of the confidence we can place in them. If we cannot do so, then the choice as to which theory, among the multitude relevant to an experiment, a negative result should be taken as falsifying is arbitrary. Lester writes: "We can now return to Callahan's suggestion that, given an experimental result that apparently refutes a theory, one can always change an auxiliary hypothesis instead of the central tenet of the theory, and so rescue the theory. Why should we do that unless we suspect that there is an error in the particular auxiliary hypothesis?" However, per Popper, we ought to believe the probability that any of our theories are true is zero, so not only should we suspect an error in an auxiliary hypothesis, we should be certain that there is one (or more).

It is certainly true that the mere observation of many white swans does not justify the proposition that all swans are white. However, if we are proceeding as Boyle advised, seeking to uncover an "invisible corporeal agent" determining the color of swans, and we believe we have found one that will cause all of them to be white, then each new instance of a white swan will rightly increase our confidence that we are on the correct track. But, as shown above, if Boyle's use of inductive inference isn't valid, then we can't falsify our theory either. Lester admits that, in thinking we have perceived a non-white swan, "we might always be mistaken." However, the plight of the strict falsificationist is far worse than that: unless he can count on the past as offering some basis for judging what he is now observing, he has no reason to suspect he might not be mistaken. Previously, similar-looking phenomena turned out to be swans, but perhaps today some of the water in the pond formed a swan-like shape and paddled around. As demonstrated by Kant, the rationality of the entire scientific enterprise pre-supposes the existence of regular causal forces in the universe. The valid points made by Hume and Popper are that we can easily be mistaken in thinking we have discovered such a force -- an observed regularity might be just a coincidental aspect of our limited sample, or a side-effect of a genuine causal force we have overlooked -- and that simply piling up conforming instances is an unreliable method for avoiding that error. But the fact that we often make mistakes does not imply that we never get it right.

A postage stamp featuring Copernicus

The Case of Copernicus

Before concluding, I want to address a peripheral error in Lester's article. He writes: "Copernicus had the insight that, if the sphere of the stars was ten times farther from the earth than had previously been believed, then the observed lack of parallax is not a problem. This is a good criticism of the parallax test of heliocentrism (though he was, of course, also accepting the refutation of his heliocentric theory that, at least implicitly, supposed they were nearer). As, at the time, scientists had no way of knowing how far away the stars really were it would have been arbitrary to give priority to the first conjecture as to their distance just because it was the first."

However, the assumed distance to the stars in Copernicus's time was not an arbitrary guess, but followed almost by necessity from the best available physical theory, that developed by Aristotle and his Greek, Arab, and Christian epigones. That theory held that the very essence of space made the existence of a vacuum impossible. Therefore, the sphere of the fixed stars had to be immediately beyond the far edge of the sphere of Saturn. Now, if Copernicus had rejected the physics of his day as a whole, and if he had offered a reasonable alternative that accounted for at least the same range of phenomena as Aristotelianism, his maneuver of positing an enormously distant stellar sphere might have met Popper's criteria. But he did neither: While remaining an orthodox Aristotelian in most respects, he rendered the whole system incoherent by placing the Sun at the centre of the world. In place of the integrated worldview he was shattering, Copernicus offered nothing but vague suggestions: that a force emanating from the Sun might be pushing the planets along in their journeys, and that the substance of each planet might have a natural affinity for its own world. He ignored the large body of "well corroborated" theories that were incompatible with heliocentrism because of the elegance he perceived in his new model. I should add that I'm not arguing that Copernicus was wrong to follow his vision -- that resolve is central to why he is rightly considered a giant figure in the history of science -- but rather that if he had followed Popper's dictates he would have rejected the great insight upon which his fame rests, and, as a consequence, he would have failed to initiate the revolution in science that heliocentrism sparked.

Lester continues: "Callahan thinks it is a big problem for the Popperian (the Popperian falsificationist, at least) that it was only after more accurate instruments were able to measure the parallax that heliocentrism became scientific. But not all theories are scientific in the sense of being empirically falsifiable. Moral, metaphysical and mathematical theories are not, for instance.... Until we can find a way to test a theory empirically it is not scientific in this sense.... One might wish to say that they were part of science more broadly conceived to include all the theories about the material world that are as yet, or currently, unfalsifiable (just as even falsifiable scientific theories have unfalsifiable aspects and assumptions). Thus much modern theoretical physics is currently unfalsifiable but is unproblematically called science nevertheless. Such labels are of no theoretical significance."

However, if we allow unfalsifiable theories to be termed scientific, then it is hard to see what weight Popper's argument about falsification carries. Some theories are falsifiable, some are not, but they can all happily co-exist in a scientific enterprise. The whole point of his criterion was, I had thought, to sort out truly scientific theories from pseudo-scientific ones, such as Marxism and Freudianism. Within Lester's scheme, it would seem we could regard the latter two as real sciences that, as of yet, just happened to contain no falsifiable content. On the other hand, if the requirement is that a theory must have at least some falsifiable aspects, then we are forced back into the strange position of excluding Copernicanism from the realm of science until the 1800s.

Conclusion

If scientific reasoning were pure deductive logic, then Popper would be correct, and induction forbidden. Unfortunately, falsification depends, as we have seen, on induction, so falsification is not available to the Popperian either. The scientist is left to whimsically choose amongst a cornucopia of "bold conjectures," everyone of which is guaranteed to be false. But I believe that the arguments presented above make a convincing case for induction, when employed with an understanding of the limitations and inescapable fallibility of inductive inference, as a perfectly valid part of scientific reasoning. Furthermore, they demonstrate that Popper himself ultimately could not avoid incorporating induction in his account of scientific method. As Bird put it, "a feature of Popper's philosophy [is that] when the going gets tough, induction is quietly called upon to help out" (1998, p. 180). And, in the end, even Popper agreed that his system contained "a whiff of induction." (Perhaps Lester is the only remaining Popperian who has not folded on this issue!)

All of us, not just scientists, rely on inductive thinking in making sense of the world in which we find ourselves. For example, Jan Lester himself recently gave me a friendly warning about my new neighbourhood in London having a high crime rate. Of course, that rate only reflects past crimes. But no previous crime is likely to affect me while I'm living there. I'm only concerned with future crimes. In deciding to caution me, Lester must have been making an inductive inference from past incidence of crime in the area to the future incidence. Furthermore, I suspect that he thinks the past prevalence of crime was due not merely a chance run of events, but is good inductive evidence for a causal factor at work in the area: many of the residents have adopted a criminal lifestyle. I congratulate him on his proper use of induction, but I urge him to improve his methodology so that it becomes as good as his method.

References

Bird, Alexander (1998) Philosophy of Science , London: UCL Press.

Cassirer, Ernst (1981) Kant's Life and Thought , trans. James Haden, New Haven and London: Yale University Press.

Popper tried to traverse a razor's edge path along a high ridge running between the two broad plains presenting less arduous approaches to conceiving science. On one side, denying any validity to induction clears the way to a full-blown skepticism about the claim that science yields any genuine knowledge about the world we occupy. On the other, a pilgrim could join with most scientists and many philosophers in regarding reliance on induction as an essential aspect of how science moves closer and closer to the truth.

But Hume, and Popper and Lester after him, have mistakenly conflated the idea that repeatedly witnessing some event B follow some event A means that B will always follow A, which we might call naïve inductivism, with inductivism tout court . Naïve inductivism contends that having seen only white swans lends credence to a law stating that all swans are white. However, that type of inductive inference was denigrated as the flawed method embraced by his Aristotelian opponents by one of Popper's prime exemplars of inductivism, Francis Bacon .

Since Hume wrote on induction, many – indeed, probably most -- philosophers have argued against his conclusion. Immanuel Kant, J.S. Mill, C.S. Peirce, Hans Reichenbach, and Carl Hempel have been among the prominent thinkers who have decided Hume did not have the final word on the topic. More recently, a number of Popper's own followers, including Paul Feyerabend, Imre Lakatos, and John Worrall have embraced Popper's verdict on induction only to later acknowledge its proper role in science .

Since Hume wrote on induction, many – indeed, probably most -- philosophers have argued against his conclusion. Immanuel Kant, J.S. Mill, C.S. Peirce, Hans Reichenbach, and Carl Hempel have been among the prominent thinkers who have decided Hume did not have the final word on the topic. More recently, a number of Popper's own followers, including Paul Feyerabend, Imre Lakatos, and John Worrall have embraced Popper's verdict on induction only to later acknowledge its proper role in science .

However, if we allow unfalsifiable theories to be termed scientific, then it is hard to see what weight Popper's argument about falsification carries. Some theories are falsifiable, some are not, but they can all happily co-exist in a scientific enterprise. The whole point of his criterion was, I had thought, to sort out truly scientific theories from pseudo-scientific ones, such as Marxism and Freudianism. Within Lester's scheme, it would seem we could regard the latter two as real sciences that, as of yet, just happened to contain no falsifiable content. On the other hand, if the requirement is that a theory must have at least some falsifiable aspects, then we are forced back into the strange position of excluding Copernicanism from the realm of science until the 1800s.